A relaxation method for reconstructing objects from noisy Xrays
 G. T. Herman
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An algorithm is presented for estimating the density distribution in a cross section of an object from Xray data, which in practice is unavoidably noisy. The data give rise to a large sparse system of inconsistent equations, not untypically 10^{5} equations with 10^{4} unknowns, with only about 1% of the coefficients nonzero. Using the physical interpretation of the equations, each equality can in principle be replaced by a pair of inequalities, giving us the limits within which we believe the sum must lie. An algorithm is proposed for solving this set of inequalities. The algorithm is basically a relaxation method. A finite convergence result is proved. In spite of the large size of the system, in the application area of interest practical solution on a computer is possible because of the simple geometry of the problem and the redundancy of equations obtained from nearby Xrays. The algorithm has been implemented, and is demonstrated by actual reconstructions.
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 Title
 A relaxation method for reconstructing objects from noisy Xrays
 Journal

Mathematical Programming
Volume 8, Issue 1 , pp 119
 Cover Date
 19751201
 DOI
 10.1007/BF01580425
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 G. T. Herman ^{(1)}
 Author Affiliations

 1. State University of New York at Buffalo, Amherst, New York, USA